Lorentz Group in Optical Sciences
Click here for Einstein's photons.
Squeezed States!
Have you seen this picture? It came from my papers. 
The picture is for Lorentzboosted extended objects in particle physics. The supporting mathematics is called the Lorentz group. This group, by now, is the standard mathematical device for quantum and classical optics.
It is by now widely established that the Wigner function is the key scientific language for quantum optics, but not many people know that those Wigner functions in optics also serve as the representation of the Lorentz groups, such as O(2,1) and O(3,2) which are the fundamental languages for the one and twomode squeezed states. When you do squeezed states, you are doing the Lorentz groups.
On this subject, with Marilyn Noz, I have written a book entitled Phase Space Picture of Quantum Mechanics.
Recently, I have been publishing papers on applications of the Lorentz group to classical ray optics, mostly in Phys. Rev. E. Those papers were also archived in Los Alamos. Some of them are listed below.
 Jones matrix formalism as a representation of the Lorentz group
ArXiv. ,
published in J. Opt. Soc. Am. A /Vol.14, No.9 page 2290 (1997).
 Stokes parameters as a Minkowskian fourvector
ArXiv.
Physical Review E (1997).  Illustratative Example of Feynman's Rest of the Universe
Am. J. Phys. [67], 61  66 (1999).
Preprint  Wigner rotations and Iwasawa decompositions in polarization optics
ArXiv.
Physical Review E (1999).
 Optics computers for spacetime symmetries
ArXiv.
presented at various conferences during the year 1999.  Interferometers and decoherence matrices
ArXiv.
Physical Review E (2000).  Iwasawa effect in multilayer optics
ArXiv.
Physical Review E (2001).  Threelenses at most in multilens system
ArXiv.
Physical Review E (2001)  Wigner rotations in laser cavities
ArXiv.
Physical Review E (2002). 
Lens optics and group contractions
ArXiv.
Physical Review E (2003).  Cyclic representations of multilayer optics
ArXiv.
Physical Review E (2003).  Physics of twobytwo matrices
ArXiv.
presented at various conferences during the year 2003.  Lorentz group in ray optics (Review Paper)
AriXiv.
Journal of Optics B: Quantum and Secmiclassical Optics, Vol. 6, S455472 (2004).  de Sitter group as a symmetry for optical decoherence
ArXiv.
Journal of Physics A (2006).  ABCD matrices as similarity transformations of Wigner matrices and periodic
systems in optics
J. Opt. Soc. Am. A, 26 30492054 (2009).  Possible Minkowskian Language in Twolevel Systems
Journal of Optics and Spectroscopy [108], 297300 (2010).
ArXiv  Optical activities as computing resources for spacetime symmetries
Journal of Modern Optics, 57, 1722 (2010).

One anlytic form for four branches of the ABCD matrix,
J. Mod. Opt. [57], 12511259 (2010).
ArXiv  Internal spacetime symmetries of particles derivable
from periodic systems in optics,
Optics and Spectroscopy [111], 731737 (2011).
ArXiv.  The Language of Twobytwo Matrices spoken by Optical Devices
19th InternationalConference on Composites or Nano Engineering, Shanghai (China 2011).
AxXivwith Roy Galuber, Robert Boyd,
Masha Chekova, and Elizabeth
Giacobino (Nuremberg 2103).  Time separation as a hidden variable in the Copenhagen school of quantum mechanics,
in Advances in Quantum Theory,
AIP Conference Series, No.1327, pp 138147 (2011).
ArXiv.  Lorentz Harmonics, Squeeze Harmonics and Their Physical Applications,
Symmerty [3], 1636 (2011).
ArXiv.  Poincaré Sphere and Decoherence Problems
Arxiv Based on an invited talk presented at the Fedorov Memorial Symposium: International Conference "Spins and Photonic Beams at Interface," dedicated to the 100th anniversary of F.I.Fedorov (Minsk, Belarus, 2011).with two big boys from Vienna
(Budapest 2013).
Helmut Rausch (left) and
Anton Zeilinger.  Dirac Matrices and Feynman's Rest of the Universe
Symmetry 4, 626  643 (2012)
ArXiv.  Lorentz Group in Ray and Polarization Optics
Chapter 9 in "Mathematical Optics: Classical, Quantum and Computational Methods" edited by Vasudevan Lakshminarayanan, Maria L. Calvo, and Tatiana Alieva (CRC Taylor and Francis, New York 2013), pp 303349.
ArXiv.  Symmetries shared by the Poincaré Group and Poincaré Sphere.
Symmetry 5, 223252 (2013).
ArXiv.  Wigner’s SpaceTime Symmetries Based on the TwobyTwo
Matrices of the Damped Harmonic Oscillators and
the Poincaré Sphere
Symmetry [6], 473515 (2014).
ArxivHeard about Feynman's rest of the universe? Click here for a story.  Poincaré Sphere and a Unified Picture of Wigner's Little Groups
Arxiv  Entropy and Temperature from Entangled Space and Time
Phys. Sci. Int. J. [4], 1015  1039 (2014).
Arxiv  Lens optics and the continuity problems of the ABCD matrix
J. Mod. Opt. [61], 161  166 (2014).
ArXiv.
My coauthors. 

Marilyn Noz in 1975 and 2006 

Sibel Baskal

Elena Georgeiva 